Abstract
Summary It has long been recognized that the mean provides an inadequate summary whereas the set of quantiles can supply a more complete description of a sample. We introduce bivariate quantile smoothing splines, which belong to the space of bilinear tensor product splines, as nonparametric estimators for the conditional quantile functions in a two-dimensional design space. The estimators can be computed by using standard linear programming techniques and can further be used as building-blocks for conditional quantile estimations in higher dimensions. For moderately large data sets, we recommend penalized bivariate B-splines as approximate solutions. We use real and simulated data to illustrate the methodology proposed.
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Schedule a callMore From: Journal of the Royal Statistical Society Series B: Statistical Methodology
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